Identifying the optimal switching point between different invasive alien species (IAS) management policies is a very complex task and policy makers are in need of modelling tools to assist them. In this paper we develop an optimal control bioeconomic model to estimate the type of optimal policy and switching point of control efforts against a spreading IAS. We apply the models to the case study of Colorado potato beetle in the UK. The results demonstrate that eradication is optimal for small initial sizes of invasion at discovery. High capacity of the agency to reduce spread velocity for several years leads to smaller total overall costs of invasion and makes eradication optimal for larger sizes of initial invasion. In many cases, it is optimal to switch from control to acceptance within the time horizon. The switching point depends on the capacity of the agency, initial size of invasion, spread velocity of the IAS and the ratio of unit cost of damage and removal. We encourage the integration of the dispersal patterns of the invader and the geometry of the invasion in the theoretical development of the economics of IAS invasion management.